CRSQ Archive

The Angular
Size of the Moon and Other Planetary Satellites: An Argument For Design

CRSQ Volume 35(1) June 1998

Danny R. Faulkner

Abstract

It previously has been
argued that the circumstances of total solar eclipses for the earth-moon
system are unique in the solar system and that this suggests design.
This is reexamined using the latest data on the many satellites now
known to exist in the solar system. This argument is shown to be stronger
than ever. Some comments about the design argument in astronomy are
made. It is suggested that discussion of the definition and application
of the design argument be pursued.

Introduction

While the sun is about
400 times larger than the moon, the moon is also approximately 400 times
closer to the earth, so that both objects extend nearly identical angular
sizes of about 1/2 degree. This causes a total solar eclipse to be a
very remarkable event, one of the most beautiful and awe- inspiring
experiences in nature, as anyone who has seen one can attest. If the
moon were slightly farther away or smaller (or the sun closer or larger
in size), total solar eclipses would not be possible. If the situation
were reversed, many of the startling features of a total solar eclipse,
such as the diamond ring effect, Bailey's beads, and prominences near
the sun's limb, would not be as readily visible. Total solar eclipses
also would be more common, making them less thrilling phenomena that
they are now.

As beautiful as total
solar eclipses are, perhaps more importantly they offer an opportunity
for scientific study of certain solar phenomenon that would be difficult
or impossible to do otherwise. For instance, the sun's chromosphere
is briefly visible at the instants when totality begins and ends. Almost
all of the energy that we receive from the sun comes from the portion
of the sun's atmosphere called the photosphere. The chromosphere is
a thin, cooler, more rarefied region of the sun's atmosphere lying just
above the photosphere. It's feeble light is usually overpowered by the
photosphere, except when the photosphere is blocked during a total eclipse.
Historically the chromosphere's emission spectrum has been studied when
it is revealed as a flash spectrum that briefly appears around the onset
and end of totality.

Lying above the chromosphere
is the solar corona, which extends a few solar diameters into space.
Only visible during totality, the pearly white corona is very rarefied,
but is at a high temperature (between one and two million °K) .How
this high temperature is maintained has remained a mystery for some
time, and some recent creationists have used its high temperature as
evidence of its recent formation. Magnetic field lines are clearly visible
in the corona, and the size and shape of the corona changes from sun
spot minimum to sun spot maximum. So the observations of the corona
during total solar eclipses provides clues to the complex magnetic interactions
taking place in the sun.

One of the first confirmations
of general relativity was the bending of star light by the sun's mass,
which could be observed only during a total solar eclipse when the images
of stars were visible near the sun's edge. Total (or near total) solar
eclipses give us a unique opportunity to gauge the relative sizes of
the sun and moon. This provides data in deciding the question of whether
the sun is shrinking, another argument that is used for the sun's recent
origin. Historical data on the locations of eclipses have allowed us
to determine the rate at which the earth's rotation is slowing because
of tidal braking. This too places an upper limit on the age of the earth-moon
system.

For generations astronomers
have traveled to exotic locations to observe total solar eclipses because
total solar eclipses are such rare events. On average a total solar
eclipse is visible from any location only once every few centuries.
Therefore without planning it is unlikely that a typical person will
ever view a total solar eclipse, let alone more than one. Whitcomb and
DeYoung (1978, p. 132-136) and Mendillo and Hart (1974) have previously
called attention to the interesting circumstance necessary for total
solar eclipses as an argument for design in the earth-moon-sun system.
More recently Englin and Howe concluded that the unique geometry of
the earth-moon system that gives us total eclipses is no accident. No
other moon in the solar system has such a close balance between the
rarity and stark beauty of eclipses. Many have no eclipses at all. In
the two decades since the work of Whitcomb and DeYoung the number of
known satellites in the solar system has nearly doubled. At the same
time the orbital parameters and measured sizes of most of the others
have been greatly improved. Let us examine the latest values to determine
how unique our moon is in this respect.

Calculation
of Ratios

Table I lists the 61 satellites
known at the time of the writing of this article. It is possible that
additional ones may be discovered or confirmed by the time that this
goes to press, but, as it will be argued later, any of those would be
unlikely to alter the conclusion given here. All data were taken from
the 1997 Astronomical Almanac. The first two columns give the names
of the satellites. The third column lists the angular size, in degrees,
of the sun at the distance of the planet from the sun. The fourth column
gives the angular size, in degrees, that each satellite has as seen
from the planet about which the satellite orbits. The angular sizes
were calculated using the average distance (semi-major axis) of each
orbit (epoch February 1, 1997). For ease in comparison, it was decided
to express each number as a simple decimal rather than in scientific
notation. The precision of each number reflects the precision of the
satellite parameters, with the uncertainty usually dominated by uncertainties
in satellite diameters. Some of the satellites are known to be oblong
rather than spherical in shape. In those cases the largest diameters
were used.

Because the orbits of
the planets and the major satellites are nearly circular, these calculated
average angular diameters are a good starting approximation. If any
satellites were discovered to have nearly the same angular diameter
as the sun, then they could be further investigated as to the conditions
of eclipse. The orbits of some of the smaller satellites are appreciably
elliptical, and so these could be further investigated as well if it
appears that eclipses could be possible near the extremes of the orbits.

Planet

Satellite

Solar
Diameter

Satellite
Diameter

Earth I

Moon

0.5331

0.5181

Mars I

Phobos

0.3499

0.165

Mars II

Deimos

0.3499

0.037

Jupiter I

Io

0.1025

0.493

Jupiter II

Europa

0.1025

0.268

Jupiter III

Ganymede

0.1025

0.2818

Jupiter IV

Callisto

0.1025

0.1461

Jupiter V

Amalthea

0.1025

0.0855

Jupiter VI

Himalia

0.1025

0.000093

Jupiter VII

Elara

0.1025

0.000037

Jupiter VIII

Pasiphae

0.1025

0.000012

Jupiter IX

Sinope

0.1025

0.000087

Jupiter X

Lysithea

0.1025

0.00018

Jupiter XI

Carme

0.1025

0.0001

Jupiter XII

Ananke

0.1025

0.000081

Jupiter XIII

Leda

0.1025

0.00008

Jupiter XIV

Thebe

0.1025

0.028

Jupiter XV

Adrastea

0.1025

0.011

Jupiter XVI

Metis

0.1025

0.018

Saturn I

Mimas

0.05573

0.121

Saturn II

Enceladus

0.05573

0.12

Saturn III

Tethys

0.05573

0.206

Saturn IV

Dione

0.05573

0.17

Saturn V

Rhea

0.05573

0.166

Saturn VI

Titan

0.05573

0.2415

Saturn VII

Hyperion

0.05573

0.0159

Saturn VIII

Iaptus

0.05573

0.0235

Saturn IX

Phoebe

0.05573

0.000973

Saturn X

Janus

0.05573

0.083

Saturn XI

Epimetheus

0.05573

0.053

Saturn XII

Helene

0.05573

0.0055

Saturn XIII

Telesto

0.05573

0.0066

Saturn XIV

Calypso

0.05573

0.0066

Saturn XV

Atlas

0.05573

0.017

Saturn XVI

Prometheus

0.05573

0.058

Saturn XVII

Pandora

0.05573

0.044

Saturn XVIII

Pan

0.05573

0.0086

Uranus I

Ariel

0.02762

0.347

Uranus II

Umbriel

0.02762

0.252

Uranus III

Titania

0.02762

0.208

Uranus IV

Oberon

0.02762

0.15

Uranus V

Miranda

0.02762

0.213

Uranus VI

Cordelia

0.02762

0.03

Uranus VII

Ophelia

0.02762

0.032

Uranus VIII

Bianca

0.02762

0.041

Uranus IX

Cressida

0.02762

0.058

Uranus X

Desdemona

0.02762

0.049

Uranus XI

Juliet

0.02762

0.075

Uranus XII

Portia

0.02762

0.094

Uranus XIII

Rosalind

0.02762

0.044

Uranus XIV

Belinda

0.02762

0.05

Uranus XV

Puck

0.02762

0.05

Neptune I

Triton

0.01761

0.437

Neptune II

Nereid

0.01761

0.00353

Neptune III

Naiad

0.01761

0.069

Neptune IV

Thalassa

0.01761

0.092

Neptune V

Despina

0.01761

0.16

Neptune VI

Galatea

0.01761

0.15

Neptune VII

Larissa

0.01761

0.162

Neptune VIII

Proteus

0.01761

0.212

Pluto I

Charon

0.01344

3.47

Table I. Planets and their satellites with their
relationships to the sun and to each other.

The best way to evaluate
the possibility, rarity, and beauty of a particular satellite's eclipses
is to compare the sizes of the apparent solar and satellite diameters.
For instance, the ratio of the moon's apparent diameter to that of the
sun is 0.9719. This means that a typical centerline eclipse tends to
be annular rather than total. An annular eclipse is one in which the
moon is too small to completely cover the sun, so that a thin ring,
or annulus, of the sun's photosphere remains visible at mid eclipse.
This is particularly true when an eclipse occurs near the moon's apogee
or the earth's perihelion. This also effects the duration of an eclipse.
The longest totalities, about seven minutes, occur at noon in the tropics,
with the earth at aphelion and the moon at perigee.

We can conclude that if
the ratio of the angular diameter of a satellite to that of the sun
is much less than one, then no total eclipse would be possible. On the
other hand, a ratio much larger than one would cause eclipses to be
very total and very frequent. As described above, both of these effects
would tend to detract from the wonder of a total eclipse, though gross
over totality would have the greater effect. Much of the beauty of a
total solar eclipse derives from the appearance of the inner corona
and the very colorful prominences, both of which are visible near the
limb (edge) of the sun. Because of the near match in angular diameters
of the moon and sun, these are visible all around the sun's limb. For
a overly total eclipse, these would only be briefly visible near the
points of second and third contact (defined below), the points where
totality begins and ends.

Table II. Satellites with satellite/solar ratios
exceeding 0.9

Name

Ratio

Name

Ratio

Jupiter I

4.81

Jupiter II

2.61

Jupiter III

2.750

Jupiter IV

1.425

Saturn I

2.17

Saturn II

2.16

Saturn III

3.70

Saturn IV

3.05

Saturn V

2.98

Saturn VI

4.333

Saturn XI

0.95

Saturn XVI

1.03

Uranus I

12.6

Uranus II

9.13

Uranus III

7.52

Uranus IV

5.42

Uranus V

7.70

Uranus VI

1.08

Uranus VII

1.16

Uranus VIII

1.47

Uranus IX

2.1

Uranus X

1.8

Uranus XI

2.7

Uranus XII

3.4

Uranus XIII

1.6

Uranus XIV

1.8

Uranus XV

3.7

Neptune I

24.82

Neptune III

3.9

Neptune IV

5.2

Neptune V

9.2

Neptune VI

8.3

Neptune VII

9.20

Neptune VIII

12.1

Pluto I

258

Table II displays the
ratios of the angular diameters (satellite/solar) for the 34 satellites
for which the ratio exceeds 0.9. It can be assumed that the other 37
satellites fail to pro- duce any total solar eclipses. As can be seen
from the second table, the ratios show that most satellites that produce
total eclipses produce ones that are overly total. The most extreme
is Pluto's moon, which has a ratio of 258. The best candidates for total
eclipses are Saturn XI (0.95), Saturn XVI (l.02), and Uranus VI (1.08)

Saturn XI and Saturn XVI
are not spherical, but are elongated, and as stated above, the longest
diameter was used to find the angular size. Most of the satellites of
the solar system are believed to follow synchronous orbits, that is,
they orbit the planets with one face toward the parent body at all times.
This is caused by a tidal interaction, and is expected to be especially
true of the small, elongated satellites. For a particular satellite
this would result in the longest diameter pointing toward the planet,
and so a smaller diameter would be the diameter needed to calculate
the angular diameter of the moon. Therefore it is unlikely that total
eclipses would occur for these two small moons. Using the largest satellite
diameter, the angular diameter of the sun, and the satellite's orbital
period, the duration of eclipse can be calculated. The duration of an
eclipse can best be expressed in terms of the times of first, second,
third, and fourth contacts. First contact is defined as the instant
when the eclipsing body first begins to block the sun's disk, and is
generally considered the beginning of the eclipse. Second contact is
the instant when the sun's disk is completely blocked, and thus marks
the onset of totality. Third contact is the end of totality, while fourth
contact is the end of the eclipse. The time from second to third contacts
is the duration of totality, and the length of the entire eclipse is
the time difference between first and fourth contacts.

For Saturn XI the duration
of eclipse is 19 seconds, while Saturn XVI has duration of 17 seconds.
These durations are for the entire eclipses from first to fourth contacts,
including the partial phases before and after any totality (or annularity).
The length of totality is impossible to calculate with the current knowledge
of the diameters of these two satellites, but it would likely be less
than one second. Such eclipse would be almost unnoticeable, let alone
enjoyable or useful for scientific study. An even worse situation prevails
for Uranus VI, with a ratio of 1.08. It is not known if it is elongated,
but given its small size, it probably is. Eclipse duration from first
to fourth contact would be less than five seconds, causing any totality
to be far less than a second.

It is obvious that the
smaller satellites of the solar system do not provide a good opportunity
for total solar eclipses, because their small sizes and rapid motion
combine to produce very short duration eclipses. It then becomes obvious
that the only hope of producing awe-inspiring eclipses is to look to
the larger satellites. Most of the larger moons produce very overly
total eclipses, but the most promising one is Jupiter IV (Callisto)
with a ratio of 1.425. Calculation shows that Callisto produces eclipses
having first to fourth contact duration of 16.6 minutes, with totality
lasting 2.9 minutes. At first look this appears to fulfill our requirements
established for rare, beautiful events. But the over totality means
that the inner corona and the prominences can only be glimpsed at narrow
ranges near the points of second and third contact. The author personally
noted that while watching the February 26, 1979 total solar eclipse
in Arborg, Manitoba with two minutes, 50 seconds of totality, prominences
were best visible on the east limb of the sun early in totality and
on the west end late in totality. This was caused by the moon's proximity
to perigee at the time, giving it a slightly larger apparent size, covering
those features first on the west limb, and then on the east limb. The
rapid motion of Callisto, combined with the more over total nature of
its eclipses, would greatly shorten the length of time that these features
would be visible.

This leads to a very subtle
effect that is hiding in these calculations. Note that for the planets
closer to the sun, total eclipses are quite rare, while for the more
distant ones, they are quite common. For instance, only the four larger
(Galilean) of the 16 satellites of Jupiter produce total eclipses, all
the satellites of Uranus and all but one of Neptune do. This is because
the angular diameter of the sun is progressively smaller as one gets
farther from the sun. This has three effects. First, it lowers the requirement
for totality. Second, it causes the eclipses to be very over total.
Third, the decreasing angular diameter diminishes the visual effect
of the eclipses. For instance, Jupiter being more than five times more
distant from the sun causes the features of the corona and prominences
to be more that five times smaller as seen from the earth. From Saturn
and beyond it is doubtful that the appearance of the sun with its photosphere
eclipsed would be that impressive or that the eclipses would be very
noticeable.

Conclusion

The doubling of the number of planetary satellites in the past two
decades has not undermined the prior conclusion of Whitcomb and De Young
and Mendillo and Hart that the earth-moon system produces uniquely beautiful
total eclipses. To the contrary, the calculations presented here demonstrate
that their conclusion is more sound than ever. Additional consideration
shows that overly total eclipses are not expected to be as spectacular
as the ones produced by our moon. Furthermore the greatly diminished
apparent size of the sun at the distances of the larger planets means
that any total solar eclipse there would lack the visual effect as seen
from the earth. The earth-moon system combines three aspects that enhances
the beauty and wonder of total solar eclipses:

A large angular size of the sun, which produces high visual resolution
of features only seen during total solar eclipses

Optimal duration of totality of up to seven minutes that allows
for maximum enjoyment

Frequency that makes total solar eclipses uncommonly rare, yet occur
often enough to be enjoyed by many

For some time this author has been concerned with the design argument
in astronomy. In discussing biological systems, the design argument
can be very powerful. For instance, if gross properties of the earth,
such as atmospheric composition or gravity were altered, life would
be impossible. If the sun's size and temperature or the earth's orbit
were different, life would again be endangered. The same can be said
for atomic properties of matter, such as the many bonds that carbon
can form, or the status of water as the universal solvent, or the unique
property of water expanding upon freezing. In short, the design argument
is a demonstration that nature must be as it is, or else life as we
know could not exist. Even evolutionary scientists have recognized this
fact and have coined the term the "anthropic principle" to
describe it (Barrow and Tipler, 1986).

Creationists often attempt to extend this very powerful design argument
to astronomical topics as discussed here. But the design argument for
the earth-moon system presented here is a much weaker one than is usually
presented for biological systems. If the earth-moon system were not
unique, or if total solar eclipses did not occur, life would not be
imperiled. In other words, while the earth-moon system may demonstrate
the Creator's imagination and concern for our enjoyment, it must not
be thus for our existence.

Just as Barrow and Tipler define weak and strong anthropic principles,
perhaps creationists should adopt the terms weak and strong in discussing
design arguments. Many of the astronomical design arguments, including
the one discussed here, would be of the weak variety. Even more basic
would be a definition of design and a methodology in consistently applying
the design argument. At this time it appears that this definition and
methodology do not exist, because most people assume that design is
readily recognized. If this is the case, then two criticisms readily
come to mind. First, many may see design where none actually exists.
Second, a sort of circular reasoning may develop where people see design
because they know that it must exist, while others of the different
persuasion fail to see the evidence.

It is hoped that other creationists join in the discussion to define
and refine the design argument.